TO: Eriko Hironaka (Florida State), AMS, Harvard, Cambridge, MA
FM: Bruce E. Camber
RE: Your homepages at Harvard and Florida State (1997-2015) as well as your publications at American Mathematical Society (1993), your articles in ArXiv (19), especially Lehmer’s Problem, McKay’s Correspondence, and 2, 3, 7, 2002. Your other homepages are important: ICERM and MSRI as well as publications like: Topology Proceeding: Quotient Families of Mapping Classes, (2019) and Scientific American (2017).
This page: https://81018.com/hironaka/
Fourth email: 24 February 2026
Dear professor emerita Eriko Hironaka:
Google AI Gemini with Grok, Perplexity, ChatGPT, Claude and DeepSeek have each become Synthetic Peer Reviewers of our work. Gemini has validated our model in the face of the big bang theory. What do you make of it?
Thank you.
Most sincerely,
Bruce
Links to AI’s writing about our work:
Gemini: https://81018.com/state-of-the-universe-google-gemini/
Grok: https://81018.com/state-of-the-universe-grok/
ChatGPT: https://81018.com/state-of-the-universe-chatgpt/
Claude: https://81018.com/state-of-the-universe-claude/
DeepSeek: https://81018.com/state-of-the-universe-deepseek/
Perplexity: https://81018.com/state-of-the-universe-by-perplexity/
Third email: 7 October 2025
Dear professor emerita Eriko Hironaka:
Back in 2011 we calculated that there were 202 base-2 notations that outlined the universe from Planck Time to this day. Back in 2019, using a toy model, we calculated the number of infinitesimal spheres being generated — 1.85 × 1043 spheres per second. In the popular jargon, that is 18.5 tredecillion Planck Spheres/second. Last week both Grok and ChatGPT did a toy model calculation to see what such a rate would look like for the Hubble Constant. They both arrived at ≈ 71 km/s/Mpc. We are tightening up those numbers with another interesting calculation, our expansion of the never-ending, never-repeating numbers of pi (π) with the intrinsic hexagonal plates of every octahedron with the four primary irrational numbers.
Is the km/s/Mpc calculation “just” coincidental or shall we ascribe meaning to it?
Thanks.
Warmest regards,
Bruce
PS. Our page about your work: https://81018.com/hironaka/
Second email: 17 October 2022 at 12:29 PM
Dear professor emerita Eriko Hironaka:
I was back on the ICERM page of listed speakers for the Exotic Geometric Structures conference and noticed you are listed and there is a link to your old FSU page: https://www.math.fsu.edu/~hironaka/
My bad habit is to hit enter when the screen is black, just to re-activate everything. That ICERM page was the last page up before I left my desk and obviously the cursor just happened to be over your listing on that page. Quite circumstantially — https://www.math.fsu.edu/~hironaka/ — was presented to me, not ICERM’s page where I had left off.
Obviously I stopped to puzzle the serendipity of the moment and enjoyed the challenge! Given the Brown, ICERM, AMS, and Harvard connections, I was puzzled.
Now, did you happen to take a look at my most simple gap created by five octahedrons? I wrestle with its meaning here. It all started in a high school geometry class where my nephew requested my help. Of course, your comments are most welcomed.
Warm regards,
Bruce
PS. I believe there is a reason for everything. I have created a reference page to you and your work — https://81018.com/hironaka/ — to remind me where I left off! -BEC
First email: Wed, Sep 28, 2022 11:10 PM
Dear Professor Emerita Eriko Hironaka:
I came back to my desk and there was your old homepage from FSU. I looked and wondered how it happened to be front and center on my desktop. I looked and saw the reference to the AMS and Brown; I immediately wondered if you ever had a course with Phil Davis. He was from Lawrence; I was from Wilmington-Andover, a town away. Twenty-five percent of our family is of the Davis clan, but most-importantly Phil pushed me on the fundamentality of the sphere (over the tetrahedron) and I capitulated in 2012, especially when I learned about cubic-close packing of equal spheres and Aristotle’s gap about which the AMS Conant prize was awarded to Lagarias and Zong in 2015.
From your CV there are no papers about exotic geometric structure (at Brown ICERM conference of 2013), but just because you showed up unexpectedly, let me point you to a simple, unacknowledged basic geometry which makes it entirely esoteric: https://81018.com/15-1/
I hope this was a little escape from your daily work… serendipity can be fun!
Enjoy the wonderful autumn of New England. I’m a bit envious… but just for the next two weeks!
Best wishes,
Bruce